Polynomial Code based Quantum Authentication: Difference between revisions
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Polynomial Code based Quantum Authentication (edit)
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==Protocol Description== | ==Protocol Description== | ||
'''Input:''' <math>\rho</math> owned by <math>\mathcal{S}</math>; <math>k</math>, <math>x</math>, <math>y</math> shared among <math>\mathcal{S}</math> and <math>\mathcal{A}</math></br></br> | |||
'''Output:''' Receiver accepts or aborts the quantum state <math>\rho^\prime</math> | |||
*'''''Encryption and encoding:''''' | |||
#<math>\mathcal{S}</math> q-encrypts the <math>m</math>-qubit original message <math>\rho</math> as <math>\tau</math> using the classical key <math>x</math> and a [[Quantum One-Time Pad | quantum one-time pad]]. This encryption is given by <math>\tau = \sigma_x^{\vec{t}_1}\sigma_z^{\vec{t}_2}\rho\sigma_z^{\vec{1}_1}\sigma_x^{\vec{t}_1}</math>, where <math>\vec{t}_1</math> and <math>\vec{t}_2</math> are <math>m</math>-bit vectors and given by the random binary key <math>x</math>. | #<math>\mathcal{S}</math> q-encrypts the <math>m</math>-qubit original message <math>\rho</math> as <math>\tau</math> using the classical key <math>x</math> and a [[Quantum One-Time Pad | quantum one-time pad]]. This encryption is given by <math>\tau = \sigma_x^{\vec{t}_1}\sigma_z^{\vec{t}_2}\rho\sigma_z^{\vec{1}_1}\sigma_x^{\vec{t}_1}</math>, where <math>\vec{t}_1</math> and <math>\vec{t}_2</math> are <math>m</math>-bit vectors and given by the random binary key <math>x</math>. | ||
#<math>\mathcal{S}</math> then encodes <math>\tau</math> according to <math>Q_k</math> with syndrome <math>y</math>, which results in the <math>n</math>-qubit state <math>\sigma</math>. This means <math>\mathcal{S}</math> encodes <math>\rho</math> in <math>n</math> qubits using <math>Q_k</math>, and then "applies" errors according to the random syndrome. | #<math>\mathcal{S}</math> then encodes <math>\tau</math> according to <math>Q_k</math> with syndrome <math>y</math>, which results in the <math>n</math>-qubit state <math>\sigma</math>. This means <math>\mathcal{S}</math> encodes <math>\rho</math> in <math>n</math> qubits using <math>Q_k</math>, and then "applies" errors according to the random syndrome. | ||
#<math>\mathcal{S}</math> sends <math>\sigma</math> to <math>\mathcal{A}</math>. | #<math>\mathcal{S}</math> sends <math>\sigma</math> to <math>\mathcal{A}</math>. | ||
*'''''Decoding and decryption:''''' | |||
#<math>\mathcal{A}</math> receives the <math>n</math> qubits, whose state is denoted by <math>\sigma^\prime</math>. | #<math>\mathcal{A}</math> receives the <math>n</math> qubits, whose state is denoted by <math>\sigma^\prime</math>. | ||
#<math>\mathcal{A}</math> measures the syndrome <math>y^\prime</math> of the code <math>Q_k</math> on his <math>n</math> qubits in state <math>\sigma^\prime</math>. | #<math>\mathcal{A}</math> measures the syndrome <math>y^\prime</math> of the code <math>Q_k</math> on his <math>n</math> qubits in state <math>\sigma^\prime</math>. | ||
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==Further Information== | ==Further Information== | ||
#[https://ieeexplore.ieee.org/abstract/document/4031361?casa_token=j0BWLVeqOZkAAAAA:T19kamFiwuoLaEbL_bESvUendLVhWzsXWZpegOxPADA_PjSobjg4Wyo8ZmV92qvfVF3Pc7_v| Ben-Or et al. (2006).] | |||
#[https://arxiv.org/pdf/0810.5375.pdf%7C| Aharonov et al. (2008).] | |||
==References== | ==References== | ||
#[https://arxiv.org/pdf/quant-ph/0205128.pdf| Barnum et al. (2002).] | #[https://arxiv.org/pdf/quant-ph/0205128.pdf| Barnum et al. (2002).] | ||
<div style='text-align: right;'>'' | |||
<div style='text-align: right;'>''Contributed by Isabel Nha Minh Le and Shraddha Singh''</div> | |||
<div style='text-align: right;'>''This page was created within the [https://www.qosf.org/qc_mentorship/| QOSF Mentorship Program Cohort 4]''</div> | |||